On the cosmological impact of a quantized scalar field

Abstract

We explicitly compute the leading order contribution to the stress-energy- momentum tensor of a scalar eld, which propagates in a Friedmann-Robertson-Walker (FRW) universe and placed in the in nite adiabatic vacuum. Since the adiabatic regularization requires removing the adiabatic zeroth, second and fourth order terms, one ends up with the sixth order expressions as the leading order contribution to the stressenergy- momentum tensor. This is a good approximation for all modes of a massive eld when the mass m of the eld is larger than the Hubble parameter H and only for the high energy (subhorizon) modes of a massless eld satisfying k > k , where k is a xed comoving momentum scale obeying k aH. To determine the magnitude of the vacuum energy density, we consider the spacetimes undergoing power-law expansion and discuss the implications for di erent cosmologically relevant backgrounds. We next consider the backreaction e ects of a quantized massless real scalar eld propogating in a FRW universe. This can be viewed as a semiclassical approach, where gravity is treated classically. We manage to obtain a new rst order di erential equation, which approximately determines the evolution of the vacuum energy density of the massless scalar eld. In this procedure, we utilize an approximation that uses the fact that the subhorizon modes evolve nearly adiabatically and the superhorizon modes freeze out. To check the validity of our method, we take xed backgrounds of cosmological interest such as de Sitter space and our ndings are shown to agree with the known results in the literature. We also analyse the possible implications of the backreaction e ects for the slow-roll in ationary models. We nd out that although these are negligible during slow-roll regime, the vacuum energy density created might have a cosmological signi cance at subsequent stages, since it decreases slower than radiation or dust.